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On Dynamic Optimality of Anti-Sandwiches

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Dynamics and Control of Advanced Structures and Machines

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 156))

Abstract

From the viewpoint of structural engineering, natural frequencies and associated eigenmodes of Anti-Sandwiches are crucial points in the context of their dynamic behavior. Here we suggest a general format for dynamic analysis by employing an extended layerwise theory. A finite-element implementation ensures the efficiency of the general solution approach. The set of control variables initially consists of originally 14 geometry and material parameters. The nature of this input enables to bound the space of parameters affecting the eigenbehavior. Due to the lack of any generic measure for optimality, we determine optimal values of the reduced parameters and propose general optimality criteria.

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References

  1. Altenbach, H.: An alternative determination of transverse shear stiffnesses for sandwich and laminated plates. Int. J. Solids Struct. 37(25), 3503–3520 (2000). https://doi.org/10.1016/S0020-7683(99)00057-8

    Article  MATH  Google Scholar 

  2. Altenbach, H., Altenbach, J., Kissing, W.: Mechanics of Composite Structural Elements, 2nd edn. Springer (2018). https://doi.org/10.1007/978-981-10-8935-0

  3. Altenbach, H., Zhilin, P.: A general theory of elastic simple shells (in russ.). Adv. Mech. 11(4), 107–148 (1988)

    Google Scholar 

  4. Aßmus, M.: Global structural analysis at photovoltaic-modules: theory, numerics, application (in german). Dissertation thesis, Otto von Guericke University Magdeburg (2018)

    Google Scholar 

  5. Aßmus, M.: Structural Mechanics of Anti-Sandwiches—An Introduction. SpringerBriefs in Continuum Mechanics. Springer International Publishing (2019). https://doi.org/10.1007/978-3-030-04354-4

  6. Aßmus, M., Bergmann, S., Eisenträger, J., Naumenko, K., Altenbach, H.: Consideration of non-uniform and non-orthogonal mechanical loads for structural analysis of photovoltaic composite structures. In: Altenbach, H., Goldstein, R.V., Murashkin, E. (eds.) Mechanics for Materials and Technologies, Advanced Structured Materials, vol. 46, pp. 73–122. Springer, Singapore (2017). https://doi.org/10.1007/978-3-319-56050-2_4

  7. Aßmus, M., Bergmann, S., Naumenko, K., Altenbach, H.: Mechanical behaviour of photovoltaic composite structures: a parameter study on the influence of geometric dimensions and material properties under static loading. Compos. Commun. 5, 23–26 (2017). https://doi.org/10.1016/j.coco.2017.06.003

    Article  Google Scholar 

  8. Aßmus, M., Jack, S., Köhl, M., Weiß, K.A.: Dynamic mechanical loads on pv-modules. In: Proceedings of the 24th European Photovoltaic Solar Energy Conference, pp. 3395–3397. Hamburg, Germany (2009). https://doi.org/10.4229/24thEUPVSEC2009-4AV.3.34

  9. Aßmus, M., Jack, S., Weiss, K.A., Koehl, M.: Measurement and simulation of vibrations of PV-modules induced by dynamic mechanical loads. Prog. Photovolt. Res. Appl. 19(6), 688–694 (2011). https://doi.org/10.1002/pip.1087

    Article  Google Scholar 

  10. Aßmus, M., Köhl, M.: Experimental investigation of the mechanical behavior of photovoltaic modules at defined inflow conditions. J. Photon. Energy 2(1), 1–11 (2012). https://doi.org/10.1117/1.JPE.2.022002

    Article  Google Scholar 

  11. Aßmus, M., Naumenko, K., Altenbach, H.: A multiscale projection approach for the coupled global-local structural analysis of photovoltaic modules. Compos. Struct. 158(-), 340–358 (2016). https://doi.org/10.1016/j.compstruct.2016.09.036

  12. Aßmus, M., Naumenko, K., Altenbach, H.: Mechanical behaviour of photovoltaic composite structures: influence of geometric dimensions and material properties on the eigenfrequencies of mechanical vibrations. Compos. Commun. 6, 59–62 (2017). https://doi.org/10.1016/j.coco.2017.10.003

    Article  Google Scholar 

  13. Aßmus, M., Naumenko, K., Altenbach, H.: Subclasses of mechanical problems arising from the direct approach for homogeneous plates. In: Altenbach, H., Chróścielewski, J., Eremeyev, V.A., Wiśniewski, K. (eds.) Recent Developments in the Theory of Shells, Advanced Structured Materials, vol. 110, pp. 43–63. Springer, Singapore (2019). https://doi.org/10.1007/978-3-030-17747-8_4

  14. Aßmus, M., Naumenko, K., Öchsner, A., Eremeyev, V.A., Altenbach, H.: A generalized framework towards structural mechanics of three-layered composite structures. Technische Mechanik 39(2), 202–219 (2019). https://doi.org/10.24352/UB.OVGU-2019-019

  15. Eisenträger, J., Naumenko, K., Altenbach, H., Meenen, J.: A user-defined finite element for laminated glass panels and photovoltaic modules based on a layer-wise theory. Compos. Struct. 133, 265–277 (2015). https://doi.org/10.1016/j.compstruct.2015.07.049

    Article  Google Scholar 

  16. Ivanov, I.V.: Analysis, modelling, and optimization of laminated glasses as plane beam. Int. J. Solids Struct. 43(22), 6887–6907 (2006). https://doi.org/10.1016/j.ijsolstr.2006.02.014

    Article  MATH  Google Scholar 

  17. Mindlin, R.D.: Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. ASME J. Appl. Mech. 18, 31–38 (1951)

    Article  Google Scholar 

  18. Naumenko, K., Eremeyev, V.A.: A layer-wise theory for laminated glass and photovoltaic panels. Compos. Struct. 112, 283–291 (2014). https://doi.org/10.1016/j.compstruct.2014.02.009

    Article  Google Scholar 

  19. Naumenko, K., Eremeyev, V.A.: A layer-wise theory of shallow shells with thin soft core for laminated glass and photovoltaic applications. Compos. Struct. 178, 434–446 (2017). https://doi.org/10.1016/j.compstruct.2017.07.007

    Article  Google Scholar 

  20. Sander, M., Ebert, M.: Vibration analysis of pv modules by laser-doppler vibrometry. In: Proceedings of the 24th European Photovoltaic Solar Energy Conference, pp. 3446–3450. Hamburg, Germany (2009). https://doi.org/10.4229/24thEUPVSEC2009-4AV.3.46

  21. Schulze, S.H., Pander, M., Naumenko, K., Altenbach, H.: Analysis of laminated glass beams for photovoltaic applications. Int. J. Solids Struct. 49(15–16), 2027–2036 (2012). https://doi.org/10.1016/j.ijsolstr.2012.03.028

    Article  Google Scholar 

  22. Weiß, K.A., Aßmus, M., Jack, S., Köhl, M.: Measurement and simulation of dynamic mechanical loads on pv-modules. In: Proceedings of the International Society for Optical Engineering (Reliability of Photovoltaic Cells, Modules, Components, and Systems II), vol. 7412, p. 03. San Diego, USA (2009). https://doi.org/10.1117/12.824859

  23. Weps, M., Naumenko, K., Altenbach, H.: Unsymmetric three-layer laminate with soft core for photovoltaic modules. Compos. Struct. 105, 332–339 (2013). https://doi.org/10.1016/j.compstruct.2013.05.029

    Article  Google Scholar 

  24. Zhilin, P.A.: Mechanics of deformable directed surfaces. Int. J. Solids Struct. 12(9), 635–648 (1976). https://doi.org/10.1016/0020-7683(76)90010-X

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät Maschinenbau, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Marcus Aßmus & Holm Altenbach

Authors
  1. Marcus Aßmus
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  2. Holm Altenbach
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Correspondence to Marcus Aßmus .

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Editors and Affiliations

  1. Institute of Technical Mechanics, Johannes Kepler University of Linz, Linz, Oberösterreich, Austria

    Hans Irschik

  2. Institute of Technical Mechanics, Johannes Kepler University of Linz, Linz, Oberösterreich, Austria

    Michael Krommer

  3. UB RAS, Institute of Continuous Media Mechanics, Perm, Russia

    Valerii P. Matveenko

  4. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    Alexander K. Belyaev

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Aßmus, M., Altenbach, H. (2022). On Dynamic Optimality of Anti-Sandwiches. In: Irschik, H., Krommer, M., Matveenko, V.P., Belyaev, A.K. (eds) Dynamics and Control of Advanced Structures and Machines. Advanced Structured Materials, vol 156. Springer, Cham. https://doi.org/10.1007/978-3-030-79325-8_1

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  • DOI: https://doi.org/10.1007/978-3-030-79325-8_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-79324-1

  • Online ISBN: 978-3-030-79325-8

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